Performance investigations of auxiliary-space Maxwell solver preconditioned iterative algorithm for controlled-source electromagnetic induction problems with electrical anisotropy

Many studies have highlighted the superior performance of iterative solvers employing the auxiliary-space Maxwell solver preconditioner in controlled-source electromagnetic induction problems featuring isotropic conductivity. The importance of considering the presence of electrical anisotropy in controlled-source electromagnetic data has been well recognized. However, considering anisotropic conductivity will impose difficulty in robustly solving the final system of linear equations as the electrical anisotropy may significantly increase its condition number and degrade the performances of iterative solvers. Whether or not iterative solvers using the auxiliary-space Maxwell solver preconditioner have similar superior performances in the case of arbitrary electrical anisotropy is still an issue to be discussed. In this study, within the framework of finite element simulation employing unstructured tetrahedral meshes, we conduct a comprehensive examination to evaluate the performance of the flexible generalized minimum residual solver with the auxiliary-space Maxwell solver preconditioner for three-dimensional controlled-source electromagnetic forward modelling problems involving arbitrary anisotropic media. Tests on synthetic one- and three-dimensional models show that our iterative scheme performs better than widely used iterative or direct solvers for controlled-source electromagnetic anisotropy forward problems. Its convergence rate is nearly independent of working frequencies, anisotropy ratio and problem size. Finally, we applied the newly developed parallel iterative scheme to the Bay du Nord reservoir in a complicated real-life offshore hydrocarbon exploration scenario characterized by anisotropic conductivity, in which our iterative scheme with an auxiliary-space Maxwell solver preconditioner has good robustness. Furthermore, we investigated how data responses at different frequencies are sensitive to the actual hydrocarbon reservoir. Our sensitivity analysis revealed that data at large measuring offsets are considerably more sensitive to the reservoir than data at shorter measuring offsets. We also assessed the impact of neglecting anisotropy in data analysis for the realistic example and found that ignoring anisotropy can lead to noticeable changes in the data. This suggests that considering anisotropy in the interpretation of the observed data is essential to guarantee the precision of controlled-source electromagnetic field surveys.